Negotiating MA Funding?

I was recently accepted into an MA program at Columbia University but have no outside scholarship funding and the price to attend would be very steep / require a significant amount of student loans. I am currently planning on attending NYU where I was offered a full-tuition scholarship for my degree so I can graduate debt free but wanted to see if I could potentially use this scholarship to negotiate with Columbia for additional scholarship funding. Has anyone successfully negotiated with Columbia University (or any university in general) for substantial graduate school funds? I've heard many people leverage other school funding at the undergraduate level but am not sure it can be translated to graduate studies.